66 citations · 292 across the 31 of their papers we have counts for
38 papers
phi-FD, a second order finite difference scheme for geometries defined by a level-set function: the Neumann case
Michel Duprez, Vanessa Lleras, Alexei Lozinski +2
We extend the phi-FD finite-difference scheme, which handles domains described by a level-set function on a Cartesian grid, to Neumann boundary conditions. The condition is relaxed…
A ϕ-FEM approach for time-dependent domains with unfitted meshes
Michel Duprez, Johan Marguet, Alexei Lozinski +1
In this work, we propose an unfitted finite element scheme to approximate the solution of the heat equation on moving domains. We use the ϕ-FEM paradigm in which the computational…
A High-Order Localized Orthogonal Decomposition Method for Heterogeneous Stokes Problems
Moritz Hauck, Alexei Lozinski
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes…
Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
J. Haydel Collins, Kangan Li, Alexei Lozinski +1
We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the - and…
A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods
Moritz Hauck, Alexei Lozinski, Roland Maier
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we a…
Phi-FEM-FNO: a new approach to train a Neural Operator as a fast PDE solver for variable geometries
Michel Duprez, Vanessa Lleras, Alexei Lozinski +2
In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we u…